Consider the system of linear equations 3x−2y+ 5z= 5, x+z= 2, x+ 2y+z= 8.   (a) Write down the augmented matrix for this system. (b) Use Gaussian elimination to find the row echelon form, stating the row operations that you use

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Consider the system of linear equations

3x−2y+ 5z= 5,

x+z= 2,

x+ 2y+z= 8.

 

(a) Write down the augmented matrix for this system.

(b) Use Gaussian elimination to find the row echelon form, stating the row operations that you use at each step.

(c) Use your answer to (b) and back substitution to find the solution.

(d) Use Gauss-Jordan elimination on your answer to (b) to obtain the reduced row echelon form, stating the row operations that you use at each step.

(e) Hence write down the solution.

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